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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2006.5
- 수록면
- 101 - 104 (4page)
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Optimal control problems involving partial differential equation are nowadays receiving much attention because of their importance in the industrial design process. Especially, the need for accurate and efficient solution methods for these problems has become an important issue.
We consider a finite element framework and multigrid methods for the case of a partial differential equation control problem with a finite number of design parameters. This present work is characterized by the fact that we extend known analytic tools for scalar elliptic problems to the case of a non symmetric system of elliptic partial differential equation, called an optimality system.
First, we prove stability of the finite element optimality system and prove the error estimates in the discrete L² norm and in the discrete H¹ norm. And then, the convergence of the multigrid method to weak solutions of the optimality system is proved. Moreover, this multigrid convergence does not require special assumptions on the boundary, it applies to polygonal domains.
We consider a finite element framework and multigrid methods for the case of a partial differential equation control problem with a finite number of design parameters. This present work is characterized by the fact that we extend known analytic tools for scalar elliptic problems to the case of a non symmetric system of elliptic partial differential equation, called an optimality system.
First, we prove stability of the finite element optimality system and prove the error estimates in the discrete L² norm and in the discrete H¹ norm. And then, the convergence of the multigrid method to weak solutions of the optimality system is proved. Moreover, this multigrid convergence does not require special assumptions on the boundary, it applies to polygonal domains.
목차
ABSTRACT
1. OPTIMAL CONTROL PROBLEM
2. THE ERROR ESTIMATES
3. MULTIGRID CONVERGENCE
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2009-410-014678669